There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow few properties like: 

• Prime numbers are positive numbers always greater than 1. 
   
• 2 is the only even prime number. 
   
• They have only two factors: 1 and the number itself. 
   
• Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
   
• As 1062 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1062 has more than two factors, it is not a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are: 

• Counting Divisors Method
   
• Divisibility Test 
   
• Prime Number Chart 
   
• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. - If there is a total count of only 2 divisors, then the number would be prime.  If the count is more than 2, then the number is composite. Let’s check whether 1062 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 1062 by 2. It is divisible by 2, so 2 is a factor of 1062.

Step 3: Divide 1062 by 3. It is divisible by 3, so 3 is a factor of 1062.

Step 4: You can simplify checking divisors by finding the root value of 1062. We then need to only check divisors up to the root value.

Step 5: Continue checking with divisors like 4, 5, 6, etc.

Since 1062 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method. 

Divisibility by 2: The number in the one's place value is 2, an even number, which means that 1062 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 1062 is 9. Since 9 is divisible by 3, 1062 is also divisible by 3. 

Divisibility by 5: The unit’s place digit is 2, so 1062 is not divisible by 5. 

Divisibility by 7: The last digit in 1062 is 2. To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (106 - 4 = 102). Since 102 is divisible by 7, 1062 is divisible by 7. 

Divisibility by 11: In 1062, the sum of the digits in odd positions is 1 + 6 = 7, and the sum of the digits in even positions is 0 + 2 = 2.

Their difference is 5, which is not divisible by 11, so 1062 is not divisible by 11. Since 1062 is divisible by more than two numbers, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write numbers in a range, for example, from 1 to 1000.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach a table of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

Since 1062 does not appear in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 1062 as 2 × 531.

Step 2: In 2 × 531, 531 is a composite number. Further, break down 531 into 3 × 177.

Step 3: Break down 177 into 3 × 59.

Step 4: 59 is a prime number.

Hence, the prime factorization of 1062 is 2 × 3 × 3 × 59.

•  Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1062 is a composite number because it is divisible by 1, 2, 3, 6, 59, 118, 177, 354, 531, and 1062.

• Sieve of Eratosthenes: A method used to find all prime numbers up to a specified integer by marking the multiples of each prime number starting from 2. 

• Divisibility Rules: A set of rules that help determine whether one number is divisible by another without performing full division. 

• Prime Factorization: The expression of a number as the product of its prime factors. 

• Co-prime Numbers: Two numbers having only 1 as their common factor are called co-prime numbers. For example, 8 and 15 are co-prime.